Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,627,000 and will produce $329,000 per year in years 5 through 15 and $518,000 per year in years 16 through 25. The U.S. gold mine will cost $2,042,000 and will produce $280,000 per year for the next 25 years. The cost of capital is 11 percent. Use Appendix D for an approximate answer but calculate your final answers using the formula and financial calculator methods. (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Australian mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.)
|
| a-1. |
Calculate the net present value for each project. (Do not round intermediate calculations and round your answers to 2 decimal places.)
|
| Net Present Value | |
| The Australian mine | $ |
| The U.S. mine | $ |
| a-2. |
Which investment should be made?
|
| Australian mine |
| b-1. |
Assume the Australian mine justifies an extra 3 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of cash flows. Calculate the new net present value given this assumption. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
|
| Net Present Value | |
| The Australian mine | $ |
| b-2. | Does the new assumption change the investment decision? |
| Yes |
rev: 11_12_2014_QC_58991
Explanation:
a-1.
| NPVAU | = −$1,627,000 + ($329,000 × {[1 − (1 / 1.1111)] / .11) / 1.114 + ($518,000 × {[1 − (1 / 1.1110)] / .11) / 1.1115 |
| = $355,684.75 | |
| NPVUS | = −$2,042,000 + $280,000 × {[1 − 1 / (1 / 1.1125)] / .11 |
| = $316,088.51 |
a-2.
Select the Australian mine. While both mines have a positive net present value, the Australian mine adds more value to the company for a smaller investment.
|
b-1.
| NPVAU | = −$1,627,000 + ($329,000 × {[1 − (1 / 1.1411)] / .14) / 1.144 + ($518,000 × {[1 − (1 / 1.1410)] / .14) / 1.1415 |
| = –$186,304.68 |
b-2.
Now the decision should be made to reject the purchase of the Australian mine and purchase the U.S. mine.
|
| Calculator solution: |
| a. |
| Australian mine: |
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CFo, enter 1,627,000 and press +|–, press the Enter key. |
| Press down arrow, enter 0, and press Enter |
| Press down arrow, enter 4, and press Enter |
| Press down arrow, enter 329,000, and press Enter. |
| Press down arrow, enter 11, and press Enter. |
| Press down arrow, enter 518,000, and press Enter. |
| Press down arrow, enter 10, and press Enter. |
| Press NPV; the calculator shows I = 0; enter 11 and press Enter. |
| Press down arrow; calculator shows NPV = 0.00. |
| Press CPT; calculator shows NPV = 355,684.75 |
U.S. mine:
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CFo, enter 2,042,000 and press +|–, press the Enter key. |
| Press down arrow, enter 280,000, and press Enter. |
| Press down arrow, enter 25, and press Enter. |
| Press NPV; the calculator shows I = 0; enter 11 and press Enter. |
| Press down arrow; calculator shows NPV = 0.00. |
| Press CPT; calculator shows NPV = 316,088.51 |
b.
| Australian mine: |
| Press the following keys: CF, 2nd, CLR WORK. |
| Calculator displays CFo, enter 1,627,000 and press +|–, press the Enter key. |
| Press down arrow, enter 0, and press Enter |
| Press down arrow, enter 4, and press Enter |
| Press down arrow, enter 329,000, and press Enter. |
| Press down arrow, enter 11, and press Enter. |
| Press down arrow, enter 518,000, and press Enter. |
| Press down arrow, enter 10, and press Enter. |
| Press NPV; the calculator shows I = 0; enter 14 and press Enter. |
| Press down arrow; calculator shows NPV = 0.00. |
| Press CPT; calculator shows NPV = –186,304.68 |
Appendix Solutions:
a-1.
| Australian mine: |
| PV of inflows | = CF1 × (PVIFA (11%, 15) – PVIFA (11%, 4)) + CF2 × (PVIFA (11%, 25) – PVIFA (11%, 15)) |
| = $329,000 × (7.191 – 3.102) + $518,000 × (8.422 – 7.191) | |
| = $1,982,939 |
| NPV | = PV of inflows – PV of outflows |
| = $1,982,939 – 1,627,000 | |
| = $355,939 |
| The U.S. Mine: |
| PV of inflows | = Cash flow × PVIFA (11%, 25) |
| = $280,000 × 8.422 | |
| = $2,358,160 |
| NPV | = PV of inflows – PV of outflows |
| = $2,358,160 – 2,042,000 | |
| = $316,160 |
b-1.
| PV of inflows | = CF1 × (PVIFA (14%, 15) – PVIFA (14%, 4)) + CF2 × (PVIFA (14%, 25) – PVIFA (14%, 15)) |
| = $329,000 × (6.142 – 2.914) + $518,000 × (6.873 – 6.142) | |
| = $1,440,670 |
| NPV | = PV of inflows – PV of outflows |
| = $1,440,670 – 1,627,000 | |
| = –$186,330.00 |
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